Question

find the least number which when added to 6 becomes exactly divisible by 16,18,24.​

Answer 1

Answer:

16 = 2^4

18 = 2×9 = 2 × 3^2

24 = 2×12 = 2 × 2 × 6 = 2^3 × 3

To find LCM, take the common multiples which have the highest power,

LCM = 2^4 × 3^2 = 16 × 9 = 144

But, we need to find the least number when added to 6 will be divisible to all 3 numbers. So, we will subtract 6 from 144,

144-6 = 138

So, the least number which when added to 6 becomes divisible by 16, 18 & 24 is 138.

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